To find out how many large pieces of fabric Doris should buy to make 7 scarves, let's follow these steps:
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Determine the total number of square pieces needed for 7 scarves. Each scarf requires 8 square pieces of fabric. Therefore, for 7 scarves: \[ \text{Total square pieces} = 7 \text{ scarves} \times 8 \text{ square pieces/scarf} = 56 \text{ square pieces} \]
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Calculate the area of one square piece of fabric. Each square piece of fabric has a side length of 4 yards. The area of one square piece is: \[ \text{Area of one square piece} = \text{side} \times \text{side} = 4 , \text{yd} \times 4 , \text{yd} = 16 , \text{yd}^2 \]
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Calculate the total area needed for 56 square pieces. The total area required for 56 square pieces is: \[ \text{Total area needed} = 56 \text{ square pieces} \times 16 \text{ yd}^2/\text{square piece} = 896 \text{ yd}^2 \]
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Calculate the area of one large piece of fabric. Each large piece of fabric has dimensions of 4 yards in length and 2 yards in width. Thus, the area of one large piece is: \[ \text{Area of one large piece} = \text{length} \times \text{width} = 4 , \text{yd} \times 2 , \text{yd} = 8 , \text{yd}^2 \]
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Determine how many large pieces of fabric are needed. To find out how many large pieces of fabric are required to cover the total area needed, we divide the total area needed by the area of one large piece: \[ \text{Number of large pieces needed} = \frac{\text{Total area needed}}{\text{Area of one large piece}} = \frac{896 , \text{yd}^2}{8 , \text{yd}^2} = 112 \]
Thus, Doris needs to buy 112 large pieces of fabric to make 7 scarves.